Description
Book SynopsisRepresents the asymptotic analysis, via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrodinger equation in the semiclassical asymptotic regime. This book exploits complete integrability to establish pointwise asymptotics for this problem's solution in the semiclassical regime.
Trade Review"Overall, this ... book [gives] a deep insight into the application of inverse scattering to equation... Most of the current books on solution theory tend to focus mainly on inverse scattering for the KdV equation, so a book that concentrates solely on the NLS equation is refreshing."--Peter Clarkson, Bulletin of the London Mathematical Society
Table of Contents*Frontmatter, pg. i*Contents, pg. v*Figures and Tables, pg. ix*Preface, pg. xi*Chapter 1. Introduction and Overview, pg. 1*Chapter 2. Holomorphic Riemann-Hilbert Problems for Solitons, pg. 13*Chapter 3. Semiclassical Soliton Ensembles, pg. 23*Chapter 4. Asymptotic Analysis of the Inverse Problem, pg. 37*Chapter 5. Direct Construction of the Complex Phase, pg. 121*Chapter 6. The Genus - Zero Ansatz, pg. 163*Chapter 7. The Transition to Genus Two, pg. 195*Chapter 8. Variational Theory of the Complex Phase, pg. 215*Chapter 9. Conclusion and Outlook, pg. 223*Appendix A. Holder Theory of Local Riemann-Hilbert Problems, pg. 229*Appendix B. Near-Identity Riemann-Hilbert Problems in L2, pg. 253*Bibliography, pg. 255*Index, pg. 259
